One of its features is that your correspondence does not transit a TMTP server operated by a third party. As with HTTP, its client connects directly to the ultimate host.
Re "users should only receive..." TMTP allows arbitrary content only from approved senders, and limited content from others (see Ping & GroupInvite). There's no manual addition to your address book on the receiver's part.
Suppose that the major email service providers and client developers agreed that from a certain date, all emails received from addresses that a user had not seen before would be truncated to 256 plaintext Unicode characters. The client UI would offer the option to whitelist that sender for future messages, which would also cause the existing message to be displayed in full.
I think we'll see better results by defining and implementing a simple new protocol that addresses all of the significant security and productivity problems with email.
Note, the current draft isn't a 1.0 candidate; there's more to come, for instance meta-messages.
At least 100M users have already seen intra-office email replaced with chatrooms. (Which, altho it solves the phishing issue, has created new productivity problems.)
TMTP doesn't have to replace SMTP overnight to be successful.
I'll leave it at that; thanks for the discussion!